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# Copyright (c) 2019-2025, Saransh Chopra, Henry Schreiner, Eduardo Rodrigues, Jonas Eschle, and Jim Pivarski.
#
# Distributed under the 3-clause BSD license, see accompanying file LICENSE
# or https://github.com/scikit-hep/vector for details.
from __future__ import annotations
import pytest
import vector
sympy = pytest.importorskip("sympy")
pytestmark = pytest.mark.sympy
x, y, z, nx, ny, nz, t = sympy.symbols("x y z nx ny nz t", real=True)
values = {x: 0.1, y: 0.2, z: 0.3, nx: 0.4, ny: 0.5, nz: 0.6}
def test_spatial_sympy():
v1 = vector.VectorSympy3D(
azimuthal=vector.backends.sympy.AzimuthalSympyXY(x, y),
longitudinal=vector.backends.sympy.LongitudinalSympyZ(z),
)
v2 = vector.VectorSympy3D(
azimuthal=vector.backends.sympy.AzimuthalSympyXY(nx, ny),
longitudinal=vector.backends.sympy.LongitudinalSympyZ(nz),
)
assert (
v1.deltaR2(v2)
== (
sympy.Mod(-sympy.atan2(ny, nx) + sympy.atan2(y, x) + sympy.pi, 2 * sympy.pi)
- sympy.pi
)
** 2
+ (
-sympy.asinh(nz / sympy.sqrt(nx**2 + ny**2))
+ sympy.asinh(z / sympy.sqrt(x**2 + y**2))
)
** 2
)
for t1 in "xyz", "xytheta", "xyeta", "rhophiz", "rhophitheta", "rhophieta":
for t2 in "xyz", "xytheta", "xyeta", "rhophiz", "rhophitheta", "rhophieta":
transformed1, transformed2 = (
getattr(v1, "to_" + t1)(),
getattr(v2, "to_" + t2)(),
)
assert transformed1.deltaR2(transformed2).subs(values) == pytest.approx(
0.116083865330319
)
def test_lorentz_sympy():
v1 = vector.VectorSympy4D(
azimuthal=vector.backends.sympy.AzimuthalSympyXY(x, y),
longitudinal=vector.backends.sympy.LongitudinalSympyZ(z),
temporal=vector.backends.sympy.TemporalSympyT(t),
)
v2 = vector.VectorSympy4D(
azimuthal=vector.backends.sympy.AzimuthalSympyXY(nx, ny),
longitudinal=vector.backends.sympy.LongitudinalSympyZ(nz),
temporal=vector.backends.sympy.TemporalSympyT(t),
)
assert (
v1.deltaR2(v2)
== (
sympy.Mod(-sympy.atan2(ny, nx) + sympy.atan2(y, x) + sympy.pi, 2 * sympy.pi)
- sympy.pi
)
** 2
+ (
-sympy.asinh(nz / sympy.sqrt(nx**2 + ny**2))
+ sympy.asinh(z / sympy.sqrt(x**2 + y**2))
)
** 2
)
for t1 in (
"xyzt",
"xythetat",
"xyetat",
"rhophizt",
"rhophithetat",
"rhophietat",
"xyztau",
"xythetatau",
"xyetatau",
"rhophiztau",
"rhophithetatau",
"rhophietatau",
):
for t2 in (
"xyzt",
"xythetat",
"xyetat",
"rhophizt",
"rhophithetat",
"rhophietat",
"xyztau",
"xythetatau",
"xyetatau",
"rhophiztau",
"rhophithetatau",
"rhophietatau",
):
tr1, tr2 = getattr(v1, "to_" + t1)(), getattr(v2, "to_" + t2)()
assert tr1.deltaR2(tr2).subs(values) == pytest.approx(0.116083865330319)
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